what engine do you have in it?
its easy to get to the started motor, might be worth, before you going taking it out, check your connection to the starter motor, specially earth connection.
if all looks fine, and as you say it never engages at first try, get someone to wack the started motor with the end of a hammer at the same time you turn the key for the first time.
if it engages, then you know its your bendix sticking.
if it is, you can remove the starter motor and try and clean it and then bench test it outside before you fit it again.
For bench testing a starter motor you need to short the contacts with a spanner, search on youtube for this, loads of videos on how to do it.
If it works as it should you should see the bendix coming out.
if it doesnt, then its time to get a new starter motor.
there's 3 bolts holding the starter motor, depending on your engine you can get to all from above, or you might get to one from underneath.
bit fiddly to get it out with downpipes and stuff in the way, but its possible.
I changed my starter motor so many times that I can do it in about 20min now
